Finite Group Databasebeta

← #26035032

Subgroups — #26035032

Order 11392.

1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.

normal subgroups only

This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152434C211yesmaximal, characteristic, complemented
2#19152409C218yesmaximal, complemented
3#19152401C218yesmaximal, complemented
4#19152396C216yesmaximal, complemented
5C2×#15668038C216yesmaximal, complemented
6#19152365C211yesmaximal, characteristic, complemented
7C2×H(5,𝔽2)×C89C211yesmaximal, characteristic, complemented
8#15668060—21no—
9#15668059C2214yescomplemented
10#15668058C2214yescomplemented
11#15668057—23no—
12C2×#13083574C2216yescomplemented
13#41×D89—24no—
14#15668043C2214yescomplemented
15#15668042C22112yescomplemented
16#15668038C22112yescomplemented
17#15668038C22124yescomplemented
18#15668037C22112yescomplemented
19#15668032C22124yescomplemented
20C2×#13083562C22112yescomplemented
21C2×#13083559C22112yescomplemented
22#15668019C2218yescomplemented
23C2×#13083558C2216yescomplemented
24H(5,𝔽2)×C89—24no—
25H(5,𝔽2)×C89C2218yescomplemented
26C2×#41×C89—21no—
27C2×#41×C89C2211yescharacteristic
28C2×#41×C89C2213yescomplemented
29C22×D4×C89—23no—
30C22×D4×C89C2213yescomplemented
31#13083575—24no—
32#13083574—26no—
33#13083574—26no—
34#13083574C2314yes—
35#13083574C23112yescomplemented
36#13083573—212no—
37C2×Dic178C2316yescomplemented
38Q8×D89—24no—
39C2×D356C2316yescomplemented
40C2×C22⋊D89—26no—
41D4×D89—212no—
42C2×C4×D89—26no—
43#13083564C2318yescomplemented
44#13083562C23124yescomplemented
45#13083561C2318yescomplemented
46#13083559C23124yescomplemented
47#13083558C2314yes—
48#13083558C23112yescomplemented
49C2×#10623494C23112yescomplemented
50C24×C89—23no—
51#41×C89—28no—
52#41×C89—26no—
53#41×C89D414yes—
54#41×C89C23112yes—
55#41×C89C2314yes—
56C2×Q8×C89D411yescharacteristic
57C2×Q8×C89C2311yescharacteristic
58C2×D4×C89—23no—
59C2×D4×C89—224no—
60C2×D4×C89—23no—
61C2×D4×C89—26no—
62C2×D4×C89D413yes—
63C2×D4×C89C23112yes—
64C2×D4×C89C2313yes—
65C22×C4×C89—23no—
66C22×C4×C89C2313yes—
67C23×C89—23no—
68C23×C89—212no—
69C23×C89—86no—
70C23×C89C2×D413yes—
71C22×D89—26no—
72Q8×C89—21no—
73Q8×C89C2×D414yes—
74Q8×C89C2412yes—
75D4×C89—212no—
76D4×C89—212no—
77D4×C89—23no—
78D4×C89C2×D4112yes—
79D4×C89C2416yes—
80C2×C4×C89—21no—
81C2×C4×C89—212no—
82C2×C4×C89C2×D413yes—
83C2×C4×C89C2×D416yes—
84C2×C4×C89C2411yescharacteristic
85C2×C4×C89C2416yes—
86C22⋊D89—212no—
87C22⋊D89—24no—
88C2×Dic89—26no—
89D356—26no—
90D356C2414yes—
91C4×D89—24no—
92C4×D89—212no—
93Dic178—26no—
94Dic178C2414yes—
95#10623494C2418yes—
96C22×C89—26no—
97C22×C89—43no—
98C22×C89—46no—
99C22×C89—812no—
100C22×C89C22×D416yes—
101C22×C89C22×D411yescharacteristic
102C2×D89—24no—
103C2×D89—86no—
104C4×C89—22no—
105C4×C89C22×D416yes—
106C4×C89C22×D411yescharacteristic
107C4×C89C2511yescharacteristic
108Dic89—24no—
109C2×C89—26no—
110C2×C89—21no—
111C2×C89—46no—
112C2×C89C23×D411yescharacteristic
113D89—44no—
114#3585—891nomaximal, Sylow
115C89#358511yescharacteristic, complemented, Sylow
116#585—891no—
117C2×H(5,𝔽2)D8911yescharacteristic, complemented
118#577—898no—
119#576—898no—
120#575—896no—
121C2×AGL(1,ℤ/8)—896no—
122#568—891no—
1232−1+4—894no—
1242−1+4—1781no—
125H(5,𝔽2)—24no—
126H(5,𝔽2)—894no—
127H(5,𝔽2)—1783no—
128H(5,𝔽2)C2×D8918yescomplemented
129C2×#41—21no—
130C2×#41—896no—
131C2×#41—1784no—
132C2×#41C2×D8911yescharacteristic
133C2×#41C2×D8913yescomplemented
134C22×D4—23no—
135C22×D4C2×D8913yescomplemented
136#137—8912no—
137#137—894no—
138AGL(1,ℤ/8)—8912no—
139AGL(1,ℤ/8)—8912no—
140AGL(1,ℤ/8)—8924no—
141#135—8924no—
142C2×SD16—8912no—
143C2×D8—8912no—
144#131—898no—
145C2×M16—896no—
146C24—23no—
147#41—28no—
148#41—26no—
149#41—8912no—
150#41—894no—
151#41—1784no—
152#41—17812no—
153#41—1786no—
154#41—1786no—
155#41C22⋊D8914yes—
156#41C22×D89112yes—
157#41C22×D8914yes—
158C2×Q8—896no—
159C2×Q8—1784no—
160C2×Q8C22⋊D8911yescharacteristic
161C2×Q8C22×D8911yescharacteristic
162C2×D4—23no—
163C2×D4—224no—
164C2×D4—23no—
165C2×D4—26no—
166C2×D4—896no—
167C2×D4—1786no—
168C2×D4—17812no—
169C2×D4C22⋊D8913yes—
170C2×D4C22×D89112yes—
171C2×D4C22×D8913yes—
172C22×C4—23no—
173C22×C4—1786no—
174C22×C4C22×D8913yes—
175Q16—898no—
176SD16—898no—
177SD16—8924no—
178D8—8924no—
179M16—894no—
180M16—8912no—
181C2×C8—8912no—
182C23—23no—
183C23—212no—
184C23—86no—
185C23—1786no—
186C23C2×C22⋊D8913yes—
187Q8—21no—
188Q8—894no—
189Q8—1786no—
190Q8C2×C22⋊D8914yes—
191Q8C23×D8912yes—
192D4—212no—
193D4—212no—
194D4—23no—
195D4—894no—
196D4—1784no—
197D4—17812no—
198D4—1786no—
199D4C2×C22⋊D89112yes—
200D4C23×D8916yes—
201C2×C4—21no—
202C2×C4—212no—
203C2×C4—1786no—
204C2×C4—1784no—
205C2×C4—17812no—
206C2×C4C2×C22⋊D8913yes—
207C2×C4C2×C22⋊D8916yes—
208C2×C4C23×D8916yes—
209C2×C4C23×D8911yescharacteristic
210C8—898no—
211C22—26no—
212C22—43no—
213C22—46no—
214C22—812no—
215C22—1784no—
216C22—7126no—
217C22C22×C22⋊D8911yescharacteristic
218C22C22×C22⋊D8916yes—
219C4—22no—
220C4—1784no—
221C4C22×C22⋊D8916yes—
222C4C22×C22⋊D8911yescharacteristic
223C4C24×D8911yescharacteristic
224C2—21no—
225C2—26no—
226C2—46no—
227C2—3564no—
228C2C23×C22⋊D8911yescharacteristic
subgroupG/H
centerC2C23×C22⋊D89
commutator, cosocleC4×C89C25
FrattiniC4C24×D89
FittingC2×H(5,𝔽2)×C89C2
socleC2×C89C23×D4
hypercenterC2×H(5,𝔽2)D89
hypocenterC89#3585
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2 ◁ C2×#41 ◁ C2×H(5,𝔽2)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19152434C2semidirect
2. #19152409C2semidirect
3. #19152401C2semidirect
4. #19152396C2semidirect
5. C2×#15668038C2semidirect
6. #19152365C2semidirect
7. C2×H(5,𝔽2)×C89C2semidirect
9. #15668059C22semidirect
10. #15668058C22semidirect
12. C2×#13083574C22semidirect
14. #15668043C22semidirect
15. #15668042C22semidirect
16. #15668038C22semidirect
17. #15668038C22semidirect
18. #15668037C22semidirect
19. #15668032C22semidirect
20. C2×#13083562C22semidirect
21. C2×#13083559C22semidirect
22. #15668019C22semidirect
23. C2×#13083558C22semidirect
25. H(5,𝔽2)×C89C22semidirect
28. C2×#41×C89C22semidirect
30. C22×D4×C89C22semidirect
35. #13083574C23semidirect
37. C2×Dic178C23semidirect
39. C2×D356C23semidirect
43. #13083564C23semidirect
44. #13083562C23semidirect
45. #13083561C23semidirect
46. #13083559C23semidirect
48. #13083558C23semidirect
49. C2×#10623494C23semidirect
115. C89#3585semidirect
117. C2×H(5,𝔽2)D89semidirect
128. H(5,𝔽2)C2×D89semidirect
133. C2×#41C2×D89semidirect
135. C22×D4C2×D89semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191524342
#191524092
#191524012
#191523962
C2×#156680382
#191523652
C2×H(5,𝔽2)×C892
#358589